Optimal Control of an HIV Model

Volume 2, Issue 4, pp 650--658 http://dx.doi.org/10.22436/jmcs.02.04.09

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Authors

H. R. Erfanian - Department of Mathematics & Statistics, University of Science and Culture, Tehran, Iran M. H. Noori Skandari - Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

Abstract

We consider an HIV model, based on optimal control, for identifying the best treatment strategy in order to maximize the healthy cells by using chemotherapies with minimum side effects. In this paper, a new approach is introduced which transform the constraints of problem to the integral constraints. By an approximation, we obtain a finite dimensional linear programming problem which give us an approximate solution for original problem.

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Keywords

• HIV Model
• Optimal Control
• Linear programming
• Measure theory
• Chemotherapy .

MSC

•  34K60
•  49K15
•  92D30
•  92C60

References

• [1] A. A. Ejigu , An Efficient Treatment Strategy for HIV Patients Using Optimal Control, African Institute for Mathematical Sciences (AIMS), South Africa (2008)
  • Google Scholar


• [2] H. R. Erfanian, A. V. Kamyad, S. Effati , The optimal method for solving continuous linear and nonlinear programs, Applied mathematical sciences, 3 (2009), 1209--1217
  • View Article
  • Google Scholar


• [3] A. B. Gumel, P. N. Shivakumar, B. M. Sahai, A mathematical model for the dynamics of HIV-1 during the typical course of infection, Nonlinear Analysis, Theory, Methods and Applications, 47 (2001), 1773--1783
  • View Article
  • Google Scholar


• [4] A. Heydari, M. H. Farahi, A. A. Heydari, Chemotherapy in an HIV model by a pair of optimal control, Proceedings of the 7th WSEAS International Conference on Simulation, Modelling and Optimization (Beijing, China), 2007 (2007), 58--63
  • View Article
  • Google Scholar


• [5] H. R. Joshi, Optimal control of an HIV immunology model, Optimal Control Applications and Methods, 23 (2002), 199--213
  • View Article
  • Google Scholar


• [6] J. Karrakchou, M. Rachik, S. Gourari, Optimal control and Infectiology: Application to an HIV/AIDS Model, Applied Mathematics and Computation, 177 (2006), 807--818
  • View Article
  • Google Scholar


• [7] A. V. Kamyad, J. E. Rubio, D. A. Wilson, An optimal control problem for the multidimensional diffusion equation with a generalized control variable, Journal of Optimization Theory and Applications, 75 (1992), 101--132
  • View Article
  • Google Scholar


• [8] A. V. Kamyad, J. E. Rubio, D. A. Wilson, The optimal control of the multidimensional diffusion equation, Journal of Optimization theory and Application, 70 (1991), 191--209
  • View Article
  • Google Scholar


• [9] J. E. Rubio, Control and Optimization the Linear Treatment of Non-linear Problems, Manchester University Press, Manchester (1986)
  • View Article
  • Google Scholar


• [10] H. Zarei, A. V. Kamyad, S. Effati, Maximizing of Asymptomatic Stage of Fast Progressive HIV Infected Patient Using Embedding Method Intelligent Control and Automation, Intelligent Control and Automation, 1 (2010), 48--58
  • View Article
  • Google Scholar